And though they don’t generally comment on these kinds of rumors, some didn’t miss an opportunity to say he’s good at the job he has now.

We first got to Bill Thompson, the former comptroller who ran against Bloomberg in 2009 — and who has officially announced that he plans to run for mayor next year — who said he’ll believe it when he hears it.

“I take Ray at his word. Commissioner Kelly has said that he’s not a candidate and I continue to believe that until I hear anything different,” he said. The Voice asked him how Kelly could impact the race if he were to run for mayor, to which Thompson replied: “Until he indicates some kind of willingness to get in, I’m not going to speculate about that.”

Before Public Advocate Bill de Blasio left City Hall after a press conference (to endorse Grace Meng for Congress), he also gave us a quick comment, praising Kelly, but declining to comment on a possible mayoral bid.

“I respect him greatly as police commissioner. I’ve worked with him for years. I like him very much,” he said. “I’m not going to talk theoretically about a theoretical candidacy in a mayoral election that’s a long way away.”

We missed Liu entirely and caught the tail end of a Post reporter’s chat with Quinn, who was rushing back inside City Hall. A rep from her office sent us a recording of that conversation, in which Quinn said that the next mayor of the city really needs Kelly as the police commissioner.

“I think whoever the next mayor of the City of New York is, they would be the luckiest mayor if Ray Kelly stayed on as Police Commissioner,” said Quinn, who is reportedly trying to put some distance between her and Mayor Bloomberg as she prepares to campaign for his job. “Anybody who wants to be the next mayor, is thinking of being the next mayor, is flirting with the idea of being the next mayor, needs Ray Kelly to stay on as their police commissioner. It’s as simple as that. I think it’s a very clear and obvious position.”

She continued her praise: “Ray Kelly has been an outstanding Police Commissioner…The truth is, go back to when crime began to go down. It wasn’t under Rudy Giuliani — it was under Ray Kelly the first time, and he doesn’t get enough credit for that. So anybody who is attracted to Ray Kelly as a leader, I understand that. He’s a terrific, terrific leader. He’s a guy who has defied all odds in keeping this city safe. Also, there is no question in my mind that if New York City is going to grow…we have to keep crime…as low as it is, if not lower, if we can get there, and the only person that can do that is Ray Kelly. But we have to make sure that’s the vision not just for the rest of the mayor’s term, not just for the four years after that, but permanently.”